Problem: Solve for $x$ and $y$ using elimination. ${2x+2y = 30}$ ${-2x-5y = -48}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $-3y = -18$ $\dfrac{-3y}{{-3}} = \dfrac{-18}{{-3}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {2x+2y = 30}\thinspace$ to find $x$ ${2x + 2}{(6)}{= 30}$ $2x+12 = 30$ $2x+12{-12} = 30{-12}$ $2x = 18$ $\dfrac{2x}{{2}} = \dfrac{18}{{2}}$ ${x = 9}$ You can also plug ${y = 6}$ into $\thinspace {-2x-5y = -48}\thinspace$ and get the same answer for $x$ : ${-2x - 5}{(6)}{= -48}$ ${x = 9}$